Realizing large, tunable dispersive shifts with parametric couplings

In recent years, parametric couplings are being deployed in a variety of applications, ranging from parametric gates, state preparation to quantum annealing. Unlike their traditional applications such as parametric amplification, these new functionalities require much stronger parametric coupling strengths that can dominate qubit decay and measurement rates. The theoretical framework to capture the effect of such strong time-dependent couplings, however, remains rudimentary. In this work, we analyze the primary building block of such a platform --- a single qubit parametrically coupled to a single-mode resonator. We establish that even this simple system can support a rich structure in dispersive shifts, that can be rendered large and tunable by choosing suitable parametric coupling drive amplitudes and frequencies. In addition, this platform can enable enhanced cavity squeezing by multi-tone parametric pumping. Our scheme can be realized with state-of-the-art circuit-QED architecture, and we discuss our early experimental efforts to support this approach.